System and method for improved channel estimation for wireless OFDM systems

ABSTRACT

In accordance with an embodiment of the present invention, a novel system and method for MMSE channel estimation are provided that take synchronization errors, either intentional or unintentional, into account during the channel estimation process. The proposed channel estimation in accordance with the present invention improves the noise averaging capability and takes advantage of channel correlation fully by removing the effect of synchronization errors during the estimation process.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional PatentApplication No. 60/754,817, filed on Dec. 29, 2005, and titled, “Systemand Method for Improved Channel Estimation for Wireless OFDM Systems”.

BACKGROUND OF THE INVENTION

Wireless communication systems have evolved substantially over the lasttwo decades. The explosive growth of the wireless communication marketis expected to continue in the future, as the demand for all types ofwireless services is increasing. Due to their ability to provide highdata rates for multimedia applications, Orthogonal Frequency DivisionMultiplexing (OFDM) is gaining a strong interest for wide-area, localarea, and personal area networks. In OFDM, carrier frequencies arechosen in such a way that there is no influence of other carriers in thedetection of the information in the carrier of interest when theorthogonality of the carrier is maintained. Maintaining thisorthogonality requires some special care for the frequency and symboltiming synchronizations. Cyclic extension of the symbols is usually usedto relax the requirements for symbol synchronization.

In wireless OFDM systems, channel estimation is an integral part of thecoherent receiver design as the performance of the receiver is greatlyaffected by the quality of the channel estimation. Extensive studies onthe topic can be found in the literature. In OFDM systems, channelestimation is frequently employed in the frequency domain after takingthe Discrete Fourier Transform (DFT) of the time synchronized digitalsamples. There are numerous approaches for estimating the ChannelFrequency Response (CFR) over the OFDM subcarriers. The directLeast-Squares (LS) estimation assumes the channel over each subcarrierto be independent. However, in practice, the CFR is often oversampledover these subcarriers, and the estimated coefficients are correlated.On the other hand, the noise in these subcarriers can be independent. Byexploiting the correlation of CFR over OFDM subcarriers, the noise canbe reduced significantly, and hense the channel estimation accuracy canbe improved. Assuming that the channel frequency correlation and noisevariance are known, Minimum Mean-Square Error (MMSE) filtering of the LSestimates has been shown to provide optimal performance under AdditiveWhite Gaussian (AWGN).

Many of the channel estimation approaches proposed in the literatureassume perfect symbol timing. However, in practice, the symbol timingused in OFDM systems is not perfect. As such, the symbol timing is oftenintentionally shifted towards the Cyclic Prefix (CP) so that anypossible error in symbol timing that might create the loss oforthogonality can be avoided. Even though this intentional bias insynchronization avoids the loss of orthogonality of the carriers andintercarrier-interference, it results in the effective CFR to be lesscorrelated due to the additional carrier-dependent phase shift.Synchronization errors in the receiver cause a linear phase rotation atthe output of the DFT block. The correlation between the channelcoefficients at different subcarriers is weakened due to this phaserotation. As a result, the performance of MMSE channel estimationdegrades significantly since the noise averaging effect will be reduced.

Accordingly, what is needed in the art is an improved system and methodfor performing Minimum Mean-Square Error (MMSE) channel estimation in anOrthogonal Frequency Division Multiplexing (OFDM) channel undersynchronization errors.

SUMMARY OF INVENTION

In accordance with a particular embodiment of the present invention, oneapproach to solving the problem of synchronization errors is byestimating the timing offset and removing the linear phase rotationcaused by it. Fortunately, the linear phase of the estimated channel inthe frequency domain is mainly due to the timing offset with less effectfrom the noise and the actual multi-path channel. So by estimating andremoving the linear phase of the estimated channel the systemperformance can be improved, especially for medium and highsignal-to-noise ration (SNR) values.

In accordance with an embodiment of the present invention, a method forimproving the Minimum Mean-Square Error (MMSE) channel estimation in anOrthogonal Frequency Division Multiplexing (OFDM) channel undersynchronization errors includes the steps of receiving data over amultipath OFDM channel, estimating a timing offset for the channel,wherein the timing offset results from synchronization errors in thechannel, estimating a linear phase rotation resulting from thesynchronization errors in the channel, wherein the linear phase rotationis dependent upon the estimated timing offset, estimating a channelfrequency response for the channel using a direct least-squaresestimation, removing the estimated linear phase rotation from theestimated channel frequency response estimate, filtering the channelfrequency response estimate for the channel using the MMSE channelestimation and then adding the estimated linear phase rotation back intothe filtered channel frequency response estimate.

In a specific embodiment, the step of estimating a timing offset for thechannel further comprises approximating the channel linear phase to thenearest value in C=[C₀C₁ . . . C_(N-CP-l)], to obtainC_({tilde over (d)}) where {tilde over (d)} is the timing offsetestimate.

In an additional embodiment, another approach to remedy the effect oftiming offsets is by increasing the channel correlation. Since thetiming offset weakens the correlation between the channel's frequencycoefficients, by removing the linear phase corresponding to differenttiming offset values and choosing the one that results in the channelwith maximum correlation we can get a very good estimate of the timingoffset. Moreover, even with a wrong timing offset assumed, we wouldstill be left with a highly correlated channel thus improving thechannel estimation performance. Another advantage to this approach isits independence of the noise level, since the noise is uncorrelatedbetween different frequency subcarriers as long as their orthogonalityis maintained.

As such, in accordance with an additional embodiment of the presentinvention, the step of estimating a timing offset resulting from thesynchronization errors of the channel further includes estimating atiming offset by identifying the timing offset that results in a maximumcorrelation of the channel in the frequency domain. In a particularembodiment, the timing offset estimating further includes calculatingthe timing offset {tilde over (d)} where:

$\overset{\sim}{d} = {\arg\;{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}{R_{\overset{\sim}{H}}(\Delta)}}}}$where R_({tilde over (H)})(Δ)=E{{tilde over (H)}_(k) ^(†){tilde over(H)}_(k+Δ)}, is the frequency-domain channel correlation function with afrequency separation Δ, {tilde over (d)} is the timing offset estimate,{tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximum correlation lagsconsidered in the identification of the timing offset with the maximumcorrelation in the frequency domain.

In accordance with the present invention, filtering the channelfrequency response for the channel using the MMSE channel estimationfurther includes estimating the channel frequency response using:{tilde over (H)}_(MMSE)=Θ_({tilde over (d)})F^(†)Θ_({tilde over (d)})⁻¹Ĥ_(LS), where F ^(†) ={tilde over (R)} _(HH) ({tilde over (R)}_(HH)+σ² I)⁻¹and where, {tilde over (H)}_(MMSE) is the MMSE channel estimation,Ĥ_(LS) is the least-squares estimate of H, F is the MMSE filter, I isN×N identity matrix, R_(HH)=E{{tilde over (H)}{tilde over (H)}^(†)},{tilde over (H)}=Θ_({tilde over (d)}) ⁻¹ H, σ² is the variance of thecomplex zero-mean white Gaussian noise vector of the channel,Θ_({tilde over (d)}) is a diagonal matrix containing the phase rotation,exp(2jπ{tilde over (d)}/N), and {tilde over (d)} is the timing offsetestimate.

The present invention provides a system for improving the MinimumMean-Square Error (MMSE) channel estimation in an Orthogonal FrequencyDivision Multiplexing (OFDM) channel under synchronization errors. Oneembodiment of the system in accordance with the present inventionincludes an OFDM receiver which includes circuitry for receiving dataover a multipath OFDM channel, circuitry for estimating a timing offsetfor the channel, wherein the timing offset results from synchronizationerrors in the channel, circuitry for estimating a linear phase rotationresulting from the synchronization errors in the channel, wherein thelinear phase rotation is dependent upon the estimated timing offset,circuitry for estimating a channel frequency response for the channelusing a direct least-squares estimation, circuitry for removing theestimated linear phase rotation from the estimated channel frequencyresponse estimate, circuitry for filtering the channel frequencyresponse estimate for the channel using the MMSE channel estimation andcircuitry the estimated linear phase rotation back into the filteredchannel frequency response estimate.

In an additional embodiment, the OFDM receiver of the system inaccordance with the present invention includes circuitry for estimatinga timing offset for the channel further by approximating the channellinear phase to the nearest value in C=[C₀C₁ . . . C_(N-CP-l)], toobtain C_({tilde over (d)}) where {tilde over (d)} is the timing offsetestimate.

The OFDM receiver may also include circuitry for estimating a timingoffset resulting from the synchronization errors of the channel byestimating a timing offset by identifying the timing offset that resultsin a maximum correlation of the channel in the frequency domain. In aspecific embodiment, the timing offset d is

${\overset{\sim}{d} = {\arg\mspace{14mu}{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}\;{R_{\overset{\sim}{H}}(\Delta)}}}}},$where R_({tilde over (H)})(Δ)=E{{tilde over (H)}_(k) ^(\){tilde over(H)}_(k+Δ)}, is the frequency-domain channel correlation function with afrequency separation Δ, {tilde over (d)} is the timing offset estimate,{tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximum correlation lagsconsidered in the identification of the timing offset with the maximumcorrelation in the frequency domain.

The OFDM receiver of the system in accordance with the present inventionmay further include circuitry for filtering the channel frequencyresponse for the channel using the MMSE channel estimation furthercomprises, estimating the channel frequency response using {tilde over(H)}_(MMSE)=Θ_({tilde over (d)})F^(\)Θ_({tilde over (d)}) ⁻¹Ĥ_(LS),where F^(\)={tilde over (R)}_(HH)({tilde over (R)}_(HH)+σ²I)⁻¹ andwhere, {tilde over (H)}_(MMSE) is the MMSE channel estimation, Ĥ_(LS) isthe least-squares estimate of H, F is the MMSE filter, I is N×N identitymatrix, R_(HH)=E{{tilde over (H)}{tilde over (H)}^(\)}, {tilde over(H)}=Θ_({tilde over (d)}) ⁻¹ H, σ² is the variance of the complexzero-mean white Gaussian noise vector of the channel,Θ_({tilde over (d)}) is a diagonal matrix containing the phase rotation,exp(2jπ{tilde over (d)}/N), and {tilde over (d)} is the timing offsetestimate.

According, the embodiments of the present invention are effective inimproving the system performance, thus allowing the system to operate athigher noise levels with less errors and better channel estimation.

As such, the present invention provides a novel system and method forMMSE channel estimation that takes synchronization errors (intentionalor not) into account. The proposed channel estimation in accordance withthe present invention improves the noise averaging capability and takesadvantage of channel correlation fully by removing the effect ofsynchronization errors during the estimation process.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the invention, reference should be made tothe following detailed description, taken in connection with theaccompanying drawings, in which:

FIG. 1 is a graphical illustration of the Channel Estimation MSEperformance with synchronization errors in accordance with an embodimentof the present invention.

FIG. 2 is a graphical illustration of the Timing offset pdf before andafter the embodiment of the present invention have been implemented inaccordance with the present invention (E_(b)/N₀=10 dB).

FIG. 3 is a graphical illustration of the Channel Estimation MSE withsynchronization errors and uniform timing offset in accordance with anembodiment of the present invention.

FIG. 4 is block diagram illustrating the components of the OFDM receiverin accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

According to a particular embodiment of the invention, we consider an Nsubcarrier OFDM system with X_(k) as the frequency domain transmittedsymbol at the kth subcarrier. The time domain complex baseband datasequence x=[x₀x₁ . . . x_(N−1)]^(T) is obtained at the output of theInverse Discrete Fourier transform (IDFT) block with X=[X₀X₁ . . .X_(N−1)]^(T) as the input. Before transmission, a cyclic prefix oflength N_(CP) is added at the beginning of the data sequence toeliminate the Inter-Symbol Interference (ISI) and preserve theorthogonality of the frequency subcarriers. The data is then transmittedover a multipath channel. The time domain channel impulse response isdescribed as a pulse train

$\begin{matrix}{{h(t)} = {\sum\limits_{i = 0}^{l - 1}{{\alpha_{i}(t)}{\delta_{i}\left( {t - \tau_{i}} \right)}}}} & (1)\end{matrix}$

Where l is the total number of paths, α_(i)(t) is complex-valuedGaussian random variable with zero mean, and τ_(i) is the delay of theith path. The CP length N_(CP) is chosen such that 0<τ_(l−1)<N_(CP)T_(S)where T_(S) is the sampling interval so that ISI will is eliminated. Thereceived signal is sampled and fed into an N-point DFT block. The outputof the DFT block isY=XH+W  (2)

Where Y is the received vector, X is a diagonal matrix containing thetransmitted signal, H is the channel vector, and W is a complexzero-mean Gaussian noise with variance σ².

When there are no synchronization errors (zero timing offset) the MMSEchannel estimation is as follows:Ĥ_(MMSE)=F^(†)Ĥ_(LS)  (3)andF ^(†) =RR _(HH)(R _(HH)+σ² I)⁻¹  (4)

Where F is the MMSE filter, I is N×N identity matrix, R_(HH)=E{HH^(†)}is the channel autocorrelation matrix (the superscript (.)^(†) denotesthe Hermitian transpose), and Ĥ_(LS) is the LS estimate of H,Ĥ _(LS) =X ⁻¹ Y=H+X ⁻¹ W  (5)

However, a timing synchronization error will cause an offset of dsamples at the input of the receiver DFT block. For no ISI, the timingoffset d should be 0≦d≦N_(CP)−l−1. Since d can have negative values, anintentional timing offset is usually added at the receiver to guaranteethat d≧0. When the timing offset is within this range, the equivalentCFR at subcarrier k is

$\begin{matrix}{{\overset{\_}{H}}_{k} = {H_{k}{\exp\left( \frac{{j2\pi}\; d\; k}{N} \right)}}} & (6)\end{matrix}$

The received frequency domain signal including the synchronization errorcan then be presented asY=X H+W=XΘ _(d) H+W  (7)where Θ_(d) is a diagonal matrix containing the phase rotationexp(j2πdk/N), k=0,1, . . . N−1. Due to this timing offset, the effectivechannel will appear to be changing at a faster rate than the actualchannel and the correlation between the channel coefficients atdifferent subcarriers will be weaker. As a result, the performance ofthe MMSE estimation will degrade.

As previously described in the background of the invention,synchronization errors in the OFDM receiver will result in a linearphase rotation that is dependent on the timing offset d. The presentinvention provides a system and method to estimate this phase rotationand reverse its effect.

The channel phase at subcarrier k∠( H _(k)=∠(H _(k))+C _(d) k  (8)where C_(d)=j2πd/N, and d=0,1, . . . N_(CP)−l−1. So, the linear phasecomponent of the effective channel is equal to (C_(d)+φ) where φ is thelinear phase introduced by the actual channel H_(k). However, the phaseof the actual channel is random with a uniform distribution between 0and π, which means that C_(d) is the dominant component in the linearphase of the effective channel. By approximating the channel linearphase to the nearest value in C=[C₀C₁ . . . C_(N-CP-l)], we obtainC_({tilde over (d)}) where {tilde over (d)} is the timing offsetestimate. The autocorrelation matrix is then given by{tilde over (R)}_(HH)+E{{tilde over (H)}{tilde over (H)}^(†)}  (9)where {tilde over (H)}=Θ_({tilde over (d)}) ⁻¹ H, andΘ_({tilde over (d)}) is a diagonal matrix containing exp(2jπ{tilde over(d)}/N). If the timing offset is perfectly estimated, then {tilde over(d)}=d and {tilde over (H)}=H which is the actual CFR. The MMSEestimation is given by{tilde over (H)}_(MMSE)=Θ_({tilde over (d)})F^(†Θ) _({tilde over (d)})⁻¹Ĥ_(LS)  (10)whereF ^(†) ={tilde over (R)} _(HH)({tilde over (R)} _(HH)+σ² I)⁻¹  (11)

As shown in (10) first the estimated phase rotation is removed from thechannel LS estimate Θ_({tilde over (d)}) ⁻¹Ĥ_(LS) and then the MMSEestimation filter F is applied. Again, if the timing offset estimationis perfect, F will be the same filter used when there are nosynchronization errors. Finally, Θ_({tilde over (d)}) is added. In otherwords, the timing offset d estimation and then the actual channel MMSEestimation steps are performed separately.

Since the synchronization errors weaken the correlation between thechannel coefficients at different subcarriers, the present inventionwill choose the timing offset resulting in a channel with maximumcorrelation. Usually, the maximum correlation is obtained when {tildeover (d)}=d. However, even if an error has been made is estimating d,the MMSE estimation will then be performed on a highly correlatedversion of the channel with less variation, thus improving the MMSEoverall performance. First, the timing offset d is found that results inthe channel with maximum correlation in the frequency domain

$\begin{matrix}{\overset{\sim}{d} = {\arg\;{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}{R_{\overset{\sim}{H}}(\Delta)}}}}} & (12)\end{matrix}$whereR _({tilde over (H)})(Δ)=E{{tilde over (H)} _(k) ^(†) {tilde over (H)}_(k+Δ)}  (13)is the frequency-domain channel correlation function with a frequencyseparation Δ, and {tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximumcorrelation lags considered. After finding the timing offset {tilde over(d)} that results in maximum correlation, the MMSE estimation iscalculated as in (9) and (10).

The system performance is expressed in terms of Mean Square Error (MSE).First, the case of no synchronization error is considered. The meansquare error at a subcarrier k is,ε_(k) =E{|Ĥ _(k) −H _(k)|²}  (14)

The average MSE is found to be,

$\begin{matrix}\begin{matrix}{ɛ = {\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}ɛ_{k}}}} \\{= {\frac{1}{N}{{Tr}\left\lbrack {S_{H} - {R_{HH}F^{\dagger}} - {F^{\dagger}R_{HH}} + {{F^{\dagger}\left( {R_{HH} + {\sigma^{2}I}} \right)}F}} \right\rbrack}}}\end{matrix} & (15)\end{matrix}$where Tr(.) denotes the trace of a matrix and S_(H) is a diagonal matrixcontaining E{|H_(k)|²}(which is equal to the diagonal elements ofR_(HH)). By substituting (4) into (15) and using the fact that R_(HH)^(†)=R_(HH),

$\begin{matrix}\begin{matrix}{ɛ = {\frac{1}{N}{{Tr}\left\lbrack {S_{H} - {{R_{HH}\left( {R_{HH} + {\sigma^{2}S_{H}}} \right)}^{- 1}R_{HH}}} \right\rbrack}}} \\{= {\frac{1}{N}{{Tr}\left( {S_{H} - {F^{\dagger}R_{HH}}} \right)}}}\end{matrix} & (16)\end{matrix}$

The channel autocorrelation matrix is obtained as follows,

$\begin{matrix}{{R_{HH}\left( {k_{1},k_{2}} \right)} = {\sum\limits_{i = 0}^{l - 1}{p_{i}{\exp\left\lbrack \frac{{- {{j2\pi}\left( {k_{1} - k_{2}} \right)}}{\mathbb{i}}}{N} \right\rbrack}}}} & (17)\end{matrix}$where p=[p₀p₁ . . . p_(l−1)] is the channel Power Delay Profile (PDP)vector. The average MSE with synchronization errors can be derived using(16) and (17) with a small modification. The channel PDP will beexchanged with the effective power delay profile p^(E), where p^(E) isthe convolution of the channel PDP and the timing offset ProbabilityDensity Function (PDF).

To evaluate the performance of the method of the present invention, anew error term γ_(d) is defined, whereγ_(d) =d−{tilde over (d)}  (18)

The significance of this term is that after removing the estimatedphase, the estimated CFR at subcarrier k is

$\begin{matrix}{{\overset{\sim}{H}}_{k} = {H_{k}{\exp\left( \frac{{j2\pi\gamma}_{d}k}{N} \right)}}} & (19)\end{matrix}$

Note the resemblance between (6) and (19). Hence, to evaluate theaverage MSE for one of the proposed methods, first p^(γ) is obtained,where p^(γ) is the convolution of the channel PDP and the PDF of γ_(d).Next, equations (16) and (17) with p^(γ) instead of p are used to obtainthe average MSE. The PDF of γ_(d) can be obtained through computersimulations.

In an exemplary embodiment, an OFDM system with N=64 frequencysubcarriers and a CP of length N_(CP)=16 samples is considered.Accordingly, a 5-tap channel with an exponential PDP such that the powerof the ith path is given by

$\begin{matrix}{{p_{i} = \frac{{\mathbb{e}}^{{- 2}i}}{\sum\limits_{i = 1}^{5}{\mathbb{e}}^{{- 2}i}}}{{i = 1},2,3,4,5}} & (20)\end{matrix}$

The timing offset d caused by the synchronization block is approximatedas a truncated Gaussian random variable with zero mean and a variance of4 samples², where −5≦d≦5. The Gaussian approximation is based on thetiming offset's statistical distribution of some of the existingsynchronization techniques. In the receiver, an intentional timingoffset of 5 samples is added to guarantee non-negative overall timingoffset. The average MSE is obtained and plotted against the ratio ofenergy per bit to the spectral noise density (E_(b)/N₀) as illustratedin FIG. 1.

The timing offset PDF for γ_(d) at different E_(b)/N₀ values is obtainedto evaluate the semi-analytical performance of the methods in accordancewith the present invention. FIG. 2 illustrates the timing offset PDFbefore 10 and after using the phase estimation method in accordance withthe present invention 15 and after using the maximum correlation method20 in accordance with the present invention at E_(b)/N₀=10 dB. Note thesignificant improvement in the timing error.

Simulation results are used to confirm the semi-analytical results shownin FIG. 1. Note that at MSE=2×10⁻³ a loss of about 5 dB is caused by thesynchronization errors. As shown, a gain of 3.5 dB is achieved using themaximum correlation method in accordance with the present invention anda gain of 2 dB is achieved using the phase estimation algorithm inaccordance with the method of the present invention. Furthermore, at lowE_(b)/N₀ values, the performance of the phase estimation method inaccordance with the present invention degrades. This is expected sincefor lower E_(b)/N₀, the contribution of the noise to the phase of theestimated channel is higher. However, this is not the case for themaximum correlation method in accordance with the present invention,since the noise (regardless of its level) is uncorrelated across theOFDM subcarriers as long as the orthogonality is maintained. In FIG. 1,it can be seen that the gain of the maximum correlation method inaccordance with the present invention is constant for different valuesof E_(b)/N₀ while the gain of the phase estimation method in accordancewith the present invention is improving with higher E_(b)/N₀. At highvalues of E_(b)/N₀, both methods give almost the same performance. FIG.3, illustrates the results in FIG. 1 as they are evaluated again, butthis time for a timing offset with uniform distribution between −5 and5. It can be seen that the improvements introduced by the methods inaccordance with the present invention hold for different timing offsetPDF. Additionally, the maximum correlation method in accordance with thepresent invention has a higher computational complexity than the phaseestimation method in accordance with the present invention.

One embodiment of the system in accordance with the present inventionincludes an OFDM receiver 30 which includes circuitry for receiving dataover a multipath OFDM channel 35, circuitry for estimating a timingoffset for the channel 40, wherein the timing offset results fromsynchronization errors in the channel, circuitry for estimating a linearphase rotation resulting from the synchronization errors in the channel45, wherein the linear phase rotation is dependent upon the estimatedtiming offset, circuitry for estimating a channel frequency response forthe channel using a direct least-squares estimation 50, circuitry forremoving the estimated linear phase rotation from the estimated channelfrequency response estimate 55, circuitry for filtering the channelfrequency response estimate for the channel using the MMSE channelestimation 60 and circuitry the estimated linear phase rotation backinto the filtered channel frequency response estimate 65.

In an additional embodiment, the OFDM receiver 30 of the system inaccordance with the present invention includes circuitry for estimatinga timing offset for the channel 40 further by approximating the channellinear phase to the nearest value in C=[C₀C₁ . . . C_(N-CP-l)], toobtain C_({tilde over (d)}) where {tilde over (d)} is the timing offsetestimate.

The OFDM receiver 30 may also include circuitry for estimating a timingoffset 40 resulting from the synchronization errors of the channel byestimating a timing offset by identifying the timing offset that resultsin a maximum correlation of the channel in the frequency domain. In aspecific embodiment, the timing offset d is

${\overset{\sim}{d} = {\arg\mspace{14mu}{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}\;{R_{\overset{\sim}{H}}(\Delta)}}}}},$where R_({tilde over (H)})(Δ)=E{{tilde over (H)}_(k) ^(\){tilde over(H)}_(k+Δ)}, is the frequency-domain channel correlation function with afrequency separation Δ, {tilde over (d)} is the timing offset estimate,{tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximum correlation lagsconsidered in the identification of the timing offset with the maximumcorrelation in the frequency domain.

The OFDM receiver 30 of the system in accordance with the presentinvention may further include circuitry for filtering the channelfrequency response for the channel using the MMSE channel estimationfurther comprises, estimating the channel frequency response 60 using{tilde over (H)}_(MMSE)=Θ_({tilde over (d)})F^(\)Θ_({tilde over (d)})⁻¹Ĥ_(LS), where F^(\)={tilde over (R)}_(HH)({tilde over (R)}_(HH)+σ²I)⁻¹and where, {tilde over (H)}_(MMSE) is the MMSE channel estimation,Ĥ_(LS) is the least-squares estimate of H, F is the MMSE filter, I isN×N identity matrix, R_(HH)E{{tilde over (H)}{tilde over (H)}^(\)},{tilde over (H)}=Θ_({tilde over (d)}) ⁻¹ H, σ² is the variance of thecomplex zero-mean white Gaussian noise vector of the channel,Θ_({tilde over (d)}) is a diagonal matrix containing the phase rotation,exp(2jπ{tilde over (d)}/N), and {tilde over (d)} is the timing offsetestimate.

The present invention considers MMSE channel estimation for OFDM systemsunder synchronization errors. The present invention provides a systemand method to combat the effect of synchronization errors and restorethe performance of the MMSE estimation. In accordance with oneembodiment of the present invention, the linear phase rotation isestimated—caused by the timing offset in the receiver—and is removedbefore applying the MMSE estimation. In an additional embodiment, thetiming offset is removed that results in the maximum correlated channel.Both embodiments exhibit a significant improvement in the MMSEestimation performance.

Additionally, a derivation is presented for the performance of the twoembodiments. Simulation results are used to check the semi-analyticalresults. Note that the phase estimation algorithm gain improves forlower noise levels because of the noise effect on the linear phaseestimation. On the other hand, the maximum correlation algorithm gain isconstant even for high noise levels since the noise is uncorrelatedbetween subcarriers. This, however, comes at the cost of highercomputational complexity.

It will be seen that the advantages set forth above, and those madeapparent from the foregoing description, are efficiently attained andsince certain changes may be made in the above construction withoutdeparting from the scope of the invention, it is intended that allmatters contained in the foregoing description or shown in theaccompanying drawings shall be interpreted as illustrative and not in alimiting sense.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed, and all statements of the scope of the invention which, as amatter of language, might be said to fall therebetween. Now that theinvention has been described,

1. A method for improving a Minimum Mean-Square Error (MMSE) channelestimation in an Orthogonal Frequency Division Multiplexing (OFDM)channel under synchronization errors, the method comprising the stepsof: receiving data over a multipath OFDM channel; estimating a timingoffset for the channel, wherein the timing offset results fromsynchronization errors in the channel; estimating a linear phaserotation resulting from the synchronization errors in the channel,wherein the linear phase rotation is dependent upon the estimated timingoffset; estimating a channel frequency response for the channel using adirect least-squares estimation; removing the estimated linear phaserotation from the estimated channel frequency response estimate;filtering the channel frequency response estimate for the channel usingthe MMSE channel estimation; and adding the estimated linear phaserotation back into the filtered channel frequency response estimate. 2.The method of claim 1, wherein the step of estimating a timing offsetfor the channel further comprises approximating a channel linear phaseto the nearest value in C=[C₀C₁ . . . C_(N-CP-l)], to obtainC_({tilde over (d)}) where {tilde over (d)} is the timing offsetestimate.
 3. The method of claim 1, wherein the step of estimating atiming offset resulting from the synchronization errors of the channelfurther comprises estimating a timing offset by identifying the timingoffset that results in a maximum correlation of the channel in thefrequency domain.
 4. The method of claim 3, wherein the step ofestimating a timing offset by identifying the timing offset that resultsin a maximum correlation of the channel in the frequency domain furthercomprises, calculating the timing offset d where:$\overset{\sim}{d} = {\arg\;{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}{R_{\overset{\sim}{H}}(\Delta)}}}}$where R_({tilde over (H)})(Δ)=E{{tilde over (H)}_(k) ^(\){tilde over(H)}_(k+Δ)}, is the frequency-domain channel correlation function with afrequency separation Δ, {tilde over (d)} is the timing offset estimate,{tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximum correlation lagsconsidered in the identification of the timing offset with the maximumcorrelation in the frequency domain.
 5. The method of claim 1, whereinthe step of filtering the channel frequency response for the channelusing the MMSE channel estimation further comprises, estimating thechannel frequency response using:{tilde over (H)}_(MMSE)Θ{tilde over (d)}F^(\)Θ_({tilde over (d)})⁻¹{tilde over (H)}_(LS) where, F ^(\) ={tilde over (R)} _(HH)({tildeover (R)} _(HH)σ² I)⁻¹ and where, {tilde over (H)}_(MMSE) is the MMSEchannel estimation, Ĥ_(LS) is the least-squares estimate of H, F is theMMSE filter, I is N×N identity matrix, R_(HH)=E{{tilde over (H)}{tildeover (H)}^(\)}, {tilde over (H)}=Θ_({tilde over (d)}) ⁻¹ H, σ² is thevariance of the complex zero-mean white Gaussian noise vector of thechannel, Θ_({tilde over (d)}) is a diagonal matrix containing the phaserotation, exp(2jπ{tilde over (d)}/N), and {tilde over (d)} is the timingoffset estimate.
 6. A method for improving a Minimum Mean-Square Error(MMSE) channel estimation in an Orthogonal Frequency DivisionMultiplexing (OFDM) channel under synchronization errors, the methodcomprising the steps of: receiving data over a multipath OFDM channel;estimating a timing offset for the channel by approximating a channellinear phase to the nearest value in C=[C₀C₁ . . . C_(N-CP-l)], toobtain C_({tilde over (d)}) where {tilde over (d)} is the timing offsetestimate and wherein the timing offset results from synchronizationerrors in the channel; estimating a linear phase rotation resulting fromthe synchronization errors in the channel, wherein the linear phaserotation is dependent upon the estimated timing offset; estimating achannel frequency response for the channel using a direct least-squaresestimation; removing the estimated linear phase rotation from theestimated channel frequency response estimate; filtering the channelfrequency response estimate for the channel using the MMSE channelestimation; and adding the estimated linear phase rotation back into thefiltered channel frequency response estimate.
 7. A method for improvinga Minimum Mean-Square Error (MMSE) channel estimation in an OrthogonalFrequency Division Multiplexing (OFDM) channel under synchronizationerrors, the method comprising the steps of: receiving data over amultipath OFDM channel; estimating a timing offset resulting from thesynchronization errors of the channel by identifying the timing offsetthat results in a maximum correlation of the channel in the frequencydomain; estimating a linear phase rotation resulting from thesynchronization errors in the channel, wherein the linear phase rotationis dependent upon the estimated timing offset; estimating a channelfrequency response for the channel using a direct least-squaresestimation; removing the estimated linear phase rotation from theestimated channel frequency response estimate; filtering the channelfrequency response estimate for the channel using the MMSE channelestimation; and adding the estimated linear phase rotation back into thefiltered channel frequency response estimate.
 8. The method of claim 7,wherein the step of estimating a timing offset by identifying the timingoffset that results in a maximum correlation of the channel in thefrequency domain further comprises, calculating the timing offset dwhere:$\overset{\sim}{d} = {\arg\;{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}{R_{\overset{\sim}{H}}(\Delta)}}}}$where R_({tilde over (H)})(Δ)=E{{tilde over (H)}_(k) ^(\){tilde over(H)}_(k+Δ)}, is the frequency-domain channel correlation function with afrequency separation Δ, {tilde over (d)} is the timing offset estimate,{tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximum correlation lagsconsidered in the identification of the timing offset with the maximumcorrelation in the frequency domain.
 9. The method of claim 1, whereinthe synchronization errors are unintentionally introduced into thechannel.
 10. The method of claim 1, wherein the synchronization errorsare intentionally introduced into the channel.
 11. A system forimproving a Minimum Mean-Square Error (MMSE) channel estimation in anOrthogonal Frequency Division Multiplexing (OFDM) channel undersynchronization errors, the system comprising an OFDM receivercomprising: circuitry for receiving data over a multipath OFDM channel;circuitry for estimating a timing offset for the channel, wherein thetiming offset results from synchronization errors in the channel;circuitry for estimating a linear phase rotation resulting from thesynchronization errors in the channel, wherein the linear phase rotationis dependent upon the estimated timing offset; circuitry for estimatinga channel frequency response for the channel using a directleast-squares estimation; circuitry for removing the estimated linearphase rotation from the estimated channel frequency response estimate;circuitry for filtering the channel frequency response estimate for thechannel using the MMSE channel estimation; and circuitry for adding theestimated linear phase rotation back into the filtered channel frequencyresponse estimate.
 12. The system of claim 11, wherein the receiverfurther comprises circuitry for estimating a timing offset for thechannel further by approximating a channel linear phase to the nearestvalue in C=[C₀C₁ . . . C_(N-CP-l)], to obtain C_({tilde over (d)}) where{tilde over (d)} is the timing offset estimate.
 13. The system of claim11, wherein the receiver further comprises circuitry for estimating atiming offset resulting from the synchronization errors of the channelby estimating a timing offset by identifying the timing offset thatresults in a maximum correlation of the channel in the frequency domain.14. The system of claim 11, wherein the receiver further comprisescircuitry for estimating a timing offset by identifying the timingoffset that results in a maximum correlation of the channel in thefrequency domain further comprises, calculating the timing offset dwhere:$\overset{\sim}{d} = {\arg\;{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}{R_{\overset{\sim}{H}}(\Delta)}}}}$where R_({tilde over (H)})(Δ)=E{{tilde over (H)}_(k) ^(\){tilde over(H)}_(k+Δ)}, is the frequency-domain channel correlation function with afrequency separation Δ, {tilde over (d)} is the timing offset estimate,{tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximum correlation lagsconsidered in the identification of the timing offset with the maximumcorrelation in the frequency domain.
 15. The system of claim 11, whereinthe receiver further comprises circuitry for filtering the channelfrequency response for the channel using the MMSE channel estimationfurther comprises, estimating the channel frequency response using:{tilde over (H)}_(MMSE)=Θ_({tilde over (d)})F^(\)Θ_({tilde over (d)})⁻¹Ĥ_(LS) where, F ^(\) ={tilde over (R)} _(HH)({tilde over (R)} _(HH)σ²I)⁻¹ and where, {tilde over (H)}_(MMSE) is the MMSE channel estimation,Ĥ_(LS) is the least-squares estimate of H, F is the MMSE filter, I isN×N identity matrix, R_(HH)=E{{tilde over (H)}{tilde over (H)}^(\)},{tilde over (H)}=Θ_({tilde over (d)}) ⁻¹ H, σ² is the variance of thecomplex zero-mean white Gaussian noise vector of the channel,Θ_({tilde over (d)}) is a diagonal matrix containing the phase rotation,exp(2jπ{tilde over (d)}/N), and {tilde over (d)} is the timing offsetestimate.
 16. A system for improving a Minimum Mean-Square Error (MMSE)channel estimation in an Orthogonal Frequency Division Multiplexing(OFDM) channel under synchronization errors, the system comprising:circuitry for receiving data over a multipath OFDM channel; circuitryfor estimating a timing offset for the channel by approximating achannel linear phase to the nearest value in C=[C₀C₁ . . . C_(N-CP-l)],to obtain C_({tilde over (d)}) where {tilde over (d)} is the timingoffset estimate and wherein the timing offset results fromsynchronization errors in the channel; circuitry for estimating a linearphase rotation resulting from the synchronization errors in the channel,wherein the linear phase rotation is dependent upon the estimated timingoffset; circuitry for estimating a channel frequency response for thechannel using a direct least-squares estimation; circuitry for removingthe estimated linear phase rotation from the estimated channel frequencyresponse estimate; circuitry for filtering the channel frequencyresponse estimate for the channel using the MMSE channel estimation; andcircuitry for adding the estimated linear phase rotation back into thefiltered channel frequency response estimate.
 17. A system for improvinga Minimum Mean-Square Error (MMSE) channel estimation in an OrthogonalFrequency Division Multiplexing (OFDM) channel under synchronizationerrors, the system comprising an OFDM receiver comprising circuitry forreceiving data over a multipath OFDM channel; circuitry for estimating atiming offset resulting from the synchronization errors of the channelby identifying the timing offset that results in a maximum correlationof the channel in the frequency domain; circuitry for estimating alinear phase rotation resulting from the synchronization errors in thechannel, wherein the linear phase rotation is dependent upon theestimated timing offset; circuitry for estimating a channel frequencyresponse for the channel using a direct least-squares estimation;circuitry for removing the estimated linear phase rotation from theestimated channel frequency response estimate; circuitry for filteringthe channel frequency response estimate for the channel using the MMSEchannel estimation; and circuitry for adding the estimated linear phaserotation back into the filtered channel frequency response estimate. 18.The system of claim 17, wherein the receiver further comprises circuitryfor estimating a timing offset by identifying the timing offset thatresults in a maximum correlation of the channel in the frequency domainfurther comprises, calculating the timing offset d where:$\overset{\sim}{d} = {\arg\;{\max\limits_{d}{\sum\limits_{\Delta = 0}^{n}{R_{\overset{\sim}{H}}(\Delta)}}}}$where R_({tilde over (H)})(Δ)=E{{tilde over (H)}_(k) ^(\){tilde over(H)}_(k+Δ)}, is the frequency-domain channel correlation function with afrequency separation Δ, {tilde over (d)} is the timing offset estimate,{tilde over (H)}=Θ_(d) ⁻¹ H and n is the maximum correlation lagsconsidered in the identification of the timing offset with the maximumcorrelation in the frequency domain.